Vanillin is an organic compound with the molecular formula \( C_8H_8O_3 \). It is a phenolic aldehyde with functional groups including an aldehyde, hydroxyl, and ether, and is the primary component of vanilla bean extract.
Structure of Vanillin:
\[\text{HO-C}_6H_3(\text{OCH}_3)\text{CHO}\]
Counting oxygen atoms and \(\pi\) electrons:
Total number of oxygen atoms = 3.
Total number of \(\pi\)-bonds = 4 (one in the carbonyl group and three in the benzene ring).
Since each \(\pi\)-bond has two \(\pi\)-electrons:
\[\text{Total number of \(\pi\)-electrons} = 4 \times 2 = 8\]
Therefore, the sum of oxygen atoms and \(\pi\)-electrons is:
\[3 + 8 = 11\]
A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass = 300 g mol$^{-1}$) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $____________ \(\times 10^{-2}\). (nearest integer)
[Given : $K_{b}$ of the solvent = 5.0 K kg mol$^{-1}$]
Assume the solution to be dilute and no association or dissociation of X takes place in solution.
Inductance of a coil with \(10^4\) turns is \(10\,\text{mH}\) and it is connected to a DC source of \(10\,\text{V}\) with internal resistance \(10\,\Omega\). The energy density in the inductor when the current reaches \( \left(\frac{1}{e}\right) \) of its maximum value is \[ \alpha \pi \times \frac{1}{e^2}\ \text{J m}^{-3}. \] The value of \( \alpha \) is _________.
\[ (\mu_0 = 4\pi \times 10^{-7}\ \text{TmA}^{-1}) \]